1. Young English horse adopted by Peg (7) : TEENAGE5. Notice excellent record at Hawaii university (7) : ADELPHI9. Intranets, perhaps, in existence for a short time (9) : TRANSIENT10. Undresses the wrong way to take a siesta (5) : SLEEP11. Self-centered person, for one, is enthralled by part of the Bible (6) : EGOIST12. Detective story writer not crazy about medication (8) : SPILLANE13. Disreputable character looks for gold in deep waters (9) : SEAMINESS16. Time, they say, is what we have (4) : OURS18. A-X victim (4) : PREY19. They make acquisitions for doctors (9) : PROCURERS22. In conclusion, old city is timeless (8) : ENDURING23. Get rid of last of grape jam (6) : SCRAPE26. Next rack holds special edition (5) : EXTRA27. Involved in endless bit of magic near end of performance (9) : INTRICATE28. Land that is cultivated until mature (7) : TILLAGE29. Wee, small hours? Not quite (7) : MINUTES